In mathematics, the Fibonacci sequence is made up from Fibonacci numbers, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are here:

\[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.\]

The Fibbonacci sequence is popular topic of research and below you can see a table with a few examples of such publicationas.

\[\begin{equation} \begin{aligned} \text{Given} \,\, f_1=1,f_2=1, \text{then}\\ f_3=f_2+f_1=1+1=2,\\ f_4=f_3+f_2=2+1=3,\\ f_5=f_4+f_3=3+2=5, \end{aligned} \end{equation}\]

# take input from the user
nterms = 10
# first two terms
n1 = 0
n2 = 1
count = 2
# check if the number of terms is valid
if(nterms <= 0) {
print("Plese enter a positive integer")
} else {
if(nterms == 1) {
print("Fibonacci sequence:")
print(n1)
} else {
print("Fibonacci sequence:")
print(n1)
print(n2)
while(count < nterms) {
nth = n1 + n2
print(nth)
# update values
n1 = n2
n2 = nth
count = count + 1
}
}
}

Here we can see an animation of spirals generated with Fibonacci sequences.

Fibonacci spirals